Solutions - Exercise 1 (D) | Number System | Class 6 Mathematics | Selina Concise Mathematics - Middle School.
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📂 Chapter 1 - Exercise 1 (D).
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# Let's Discuss :
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# Estimation :
Estimation means to make a rough idea about quantities, cost, size, population, etc.
E.g.
(i) Cost of construction of a building is estimated to be 5 crores.
(ii) Population of a town in year 2025 is estimated around 25 lakhs.
# Approximation :
Approximation means rounding off the given quantity (number) to the nearest Ten, Hundred, Thousand, etc.
E.g.
(i) If Rohan cycled 2.8 km it is approximated to 3 km.
(ii) Price of a mobile phone is ₹24,750 which is approximated to ₹25,000.
📌Note : Approximation means nearest to actual amount or value.
# Rounding Off Numbers :
(a) Rounding off to the nearest 10 :
Rule 1 : If the digit at ones place is less than 5 (i.e. 1, 2, 3 and 4) then replace ones digit by 0, and keep the other digits as they are.
E.g.
541 to the nearest ten is 540.932 to the nearest ten is 930.753 to the nearest ten is 750.864 to the nearest ten is 860.
Rule 2 : If the digit at ones place is 5 or more than 5 (i.e. 5, 6, 7, 8 and 9) then replace ones digit by 0, and increase the tens digit by 1 and keep the other digits as they are.
E.g.
545 to the nearest ten is 550.936 to the nearest ten is 940.757 to the nearest ten is 760.868 to the nearest ten is 870.279 to the nearest ten is 280.
(b) Rounding off to the nearest 100 :
Rule 1 : If the digit at tens place is less than 5 (i.e. 1, 2, 3 and 4) then replace ones and tens digit by 0, and keep the other digits as they are.
E.g.
514 to the nearest hundred is 500.923 to the nearest hundred is 900.734 to the nearest hundred is 700.845 to the nearest hundred is 800.
Rule 2 : If the digit at tens place is 5 or more than 5 (i.e. 5, 6, 7, 8 and 9) then replace ones and tens digit by 0, and increase the hundreds digit by 1 and keep the other digits as they are.
E.g.
4352 to the nearest hundred is 4400.3961 to the nearest hundred is 4000.2376 to the nearest hundred is 2400.1685 to the nearest hundred is 1700.5291 to the nearest hundred is 5300.
(c) Rounding off to the nearest 1000 :
Rule 1 : If the digit at hundreds place is less than 5 (i.e. 1, 2, 3 and 4) then replace ones, tens and hundreds digit by 0, and keep the other digits as they are.
E.g.
5146 to the nearest thousand is 5000.9232 to the nearest thousand is 9000.7341 to the nearest thousand is 7000.8453 to the nearest thousand is 8000.
Rule 2 : If the digit at hundreds place is 5 or more than 5 (i.e. 5, 6, 7, 8 and 9) then replace ones and tens and hundreds digit by 0, and increase the thousands digit by 1 and keep the other digits as they are.
E.g.
4523 to the nearest thousand is 5000.3612 to the nearest thousand is 4000.2764 to the nearest thousand is 3000.1857 to the nearest thousand is 2000.5918 to the nearest thousand is 6000.
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-- EXERCISE - 1 (D) --
Q1. Round off (approximate) each of the following to the nearest ten :
(i) 62
Ans. 60
(ii) 265
Ans. 270
(iii) 543
Ans. 540
(iv) 8261
Ans. 8260
(v) 6296
Ans. 6300
(vi) 3998
Ans. 4000
(vii) 72396
Ans. 72400
Q2. Round off (approximate) each of the following to the nearest hundred :
(i) 748
Ans. 700
(ii) 784
Ans. 800
(iii) 2667
Ans. 2700
(iv) 5432
Ans. 5400
(v) 6998
Ans. 7000
(vi) 59997
Ans. 60000
Q3. Round off (approximate) each of the following to the nearest thousand :
(i) 6475
Ans. 6000
(ii) 6732
Ans. 7000
(iii) 25352
Ans. 25000
(iv) 32568
Ans. 33000
(v) 9948
Ans. 10000
(vi) 89994
Ans. 90000
Q4. Round off (approximate) :
(i) 578 to the nearest ten.
Ans. 580
(ii) 578 to the nearest hundred.
Ans. 600
(iii) 4327 to the nearest thousand.
Ans. 4000
(iv) 32974 to the nearest ten thousand.
Ans. 30,000
(v) 27487 to the nearest ten thousand.
Ans. 30,000
Q5. Round off (approximate) each of the following to the nearest ten, nearest hundred and nearest thousand.
(i) 864
Solution :
Nearest Ten = 860
Nearest Hundred = 900
Nearest Thousand = 1000
(ii) 1249
Solution :
Nearest Ten = 1250
Nearest Hundred = 1200
Nearest Thousand = 1000
(iii) 54,547
Solution :
Nearest Ten = 54,550
Nearest Hundred = 54,500
Nearest Thousand = 55,000
(iv) 68,076
Solution :
Nearest Ten = 68,080
Nearest Hundred = 68,100
Nearest Thousand = 68,000
(v) 56,293
Solution :
Nearest Ten = 56,290
Nearest Hundred = 56,300
Nearest Thousand = 56,000
(vi) 7,293
Solution :
Nearest Ten = 7,290
Nearest Hundred = 7,300
Nearest Thousand = 7,000
(vii) 89,24,379
Solution :
Nearest Ten = 89,24,380
Nearest Hundred = 89,24,400
Nearest Thousand = 89,24,000
Q6. Approximate each of the following to the nearest ten :
(i) ₹562
Ans. ₹560
(ii) 837 m
Ans. 840 m
(iii) 545 cm
Ans. 550 cm
(iv) ₹27
Ans. ₹30
Q7. List all the natural numbers which can be rounded off to 30.
Ans. Natural numbers which can be rounded off to 30 are 25, 26, 27, 28, 29, 31, 32, 33, 34.
Q8. List all the whole numbers which are approximate to 50.
Ans. Whole numbers which are approximate to 50 are 45, 46, 47, 48, 49, 51, 52, 53, 54.
Q9. Write the smallest and the largest numbers which are rounded off to 90.
Ans. Smallest number which can be rounded off to 90 is 85 and Largest number which can be rounded off to 90 is 94.
Q10. Write the smallest and the largest numbers which are approximate to 130.
Ans. Smallest number which can be approximate to 130 is 125 and Largest number which can be approximate to 130 is 134.
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